Question: $f(x) = 6x-3(g(x))$ $g(x) = -2x+6$ $ g(f(-5)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(-5)$ . Then we'll know what to plug into the outer function. $f(-5) = (6)(-5)-3(g(-5))$ To solve for the value of $f$ , we need to solve for the value of $g(-5)$ $g(-5) = (-2)(-5)+6$ $g(-5) = 16$ That means $f(-5) = (6)(-5)+(-3)(16)$ $f(-5) = -78$ Now we know that $f(-5) = -78$ . Let's solve for $g(f(-5))$ , which is $g(-78)$ $g(-78) = (-2)(-78)+6$ $g(-78) = 162$